Roughness

The roughness is the degree of unevenness of a solid surface. The degree of roughness affects the wettability of a solid.

Background

Measures of the roughness of a solid include:

  • The roughness coefficient r’, which specifies the ratio of the actual surface area to the geometrically projected surface area.
  • The mean roughness, which specifies the mean distance of the actual height of the surface from a virtual mean height line.

Roughness and wettability

As a high roughness is accompanied by a large surface area, the roughness has an effect on the wettability of a solid and on the contact angle of a liquid. The following applies:

If a liquid forms contact angles of less than 90° on a smooth solid, the solid is wettable. The contact angle is smaller on a rough surface of the same material. This effect is used in the Wilhelmy plate method, for example, in which the platinum plate is roughened in order to improve the wetting. According to Wenzel, the following relationship between roughness and contact angle applies for the region below 90°:

cosθ* = r'cosθ

θ* = Measured contact angle; θ = Young contact angle; r’ = Roughness coefficient;

  • If a liquid forms contact angles of greater than 90° on a smooth solid, the solid is not wettable. The contact angle is larger on a rough surface of the same material. Self-cleaning, ultrahydrophobic surfaces (lotus effect) are generally produced by supplementing the poor wettability of a material with low surface free energy by providing a rough surface texture.